Globally, the U.S., U.K. and Germany are considered the top university destinations, with 51 percent ranking the U.S. in their top three for quality of education, compared with 38 percent for the U.K. and 27 percent for Germany, the survey found.

But U.S. parents are less enthusiastic than their global counterparts, with 37 percent saying they believe their country's education system is worse than the best education overseas, the report said. Only 33 percent of American parents said they think their country's education quality is better than the best overseas, HSBC's survey said.

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Their top pick was Japan, followed by the U.S., with China taking the No.3 spot, according to the survey.

Chinese parents played the reciprocal view, pointing toward the U.S. as a top pick, while 44 percent said they believed their home country's education quality was worse than what was available overseas, it said.

"Parents in the USA and China rate each other's educational systems highly," the report said. "Over seven in 10 (73 percent) Chinese parents put USA in their top three, with 39 percent of parents in the USA thinking the same about Chinese education."

To be sure, parents in some countries take a lot of pride in their home-grown schools.

Singaporean parents are among the biggest cheerleaders for their home teams, with a whopping 75 percent saying the city-state's schools offer the best education and only 6 percent saying the quality was worse than overseas options, according to the survey.

Home-grown schools are also popular among Indian parents, with 55 percent believing they offer the best quality, the survey said.

"However, their local pride is not shared by parents in other countries," the report said. Globally, only 5 percent put India and 10 percent put Singapore in their top three for providing the highest quality education, according to the survey.

Overall, the idea of sending their children abroad for a university education gets a thumbs up from parents around the globe, with over 74 percent saying they would consider it, according to the survey. Asian parents are even more enthusiastic, with Indonesian parents the most keen, with 92 percent considering the option, the report said.